 # 9 Fisher's Exact - Review: Fishers Exact Test Contingency...

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Review: Fisher’s Exact TestContingency tables are used to summarize data from two or morecategorical variables. The simplest contingency table is a 2×2table for two binary variables.The2×2tables are widely usedin practice.The most common hypothesis testing for contingency tables is totestwhether the categorical variables are independent or not,e.g., whether the row and column variables are independent in a2×2 table.H0: the variables are independent,H1:the variables are notindependent.
Review: Fisher’s Exact TestThe usualχ2test requires that the sample size (or counts) to belarge.If the sample size (or counts) are small, theχ2test mayperform poorly, i.e., a 5% significance level may have an actualsignificance level higher than 5%.Recall: Significance level = P(type I error) = P(rejectH0|H0holds).We can usecomputer simulationto evaluate the performance of atest: we simulate many datasets (underH0) and then check howoften the test rejects
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Term
Winter
Professor
liang wu
Tags
Statistical hypothesis testing, 5, Fisher s exact test, Fisher s method, exact test

Unformatted text preview: H when H holds (i.e., whether the actual signiﬁcance level is close to the nominal signiﬁcance level). When the sample size (or counts) are small, the Fisher’s exact test can be used, which is better than the χ 2 test for small samples. Summary: Fisher’s Exact Test The Fisher’s exact test computes the exact p-value by performing probability calculations conditioning on the marginal totals being ﬁxed , i.e., if the marginal totals are ﬁxed, what is the probability of observing the data or more extreme when H holds . In general, the exact p-value of a Fisher’s exact test can be obtained using the hyper-geometric distribution. The Fisher’s exact test is only used for 2 × 2 tables. Fisher’s exact test The Fisher’s exact test is preferred when the sample size is small. When the sample size is large, the χ 2 test may still be more desirable....
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